Remark 4

Tag 0DJR, permanent. Cite it as [Bourbaki, Tag 0DJR].

Algebra, chapter IX, § 1. Formes sesquilinéaires

Give an example of a bilinear form $\Phi$ defined on a product $E \times F$ of two vector spaces, such that $d_\Phi$ is bijective, $s_\Phi$ injective but not bijective (take $E$ of infinite dimension and $F$ equal to the dual $E^*$ of $E$ ; cf. Chap. II, § 5, exer. 3).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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